The rulers have an ivory layer at the top,
in which the 20 alphabets are engraved in black.
Each ruler is marked with a red number
from 0 to 9. The upper 10 alphabets have their number at the
top, whilst the lower alphabets have it at the bottom. Two
transparent windows
are used to read the plain text and cipher text letters.

The design was covered by patents FR 461,217
and GB 23,204,
both filed by Georges Lugagne.
When unused, the device is stored in a purpose made
storage box with dark red velvet lining.
The storage case is made of wood and is covered with
black bookbinding linen, that also acts as the rear hinge. At the front
edge the name of the manufacturer, BARBOTHEU,
is impressed in golden letters.
When closed, the case is locked by a metal rod
that is pushed-in from the front right.

The diagram below shows how the Transpositeur was used for coding and
decoding messages. The operator would first set the pre-arranged
daily key, by placing the rulers in the proper order.
Note that the upper rulers can be scrambled independently from the lower ones.
Messages were coded 10 characters at a time.
In the example below, the message ATTACKNOW
is being read.

The device consists of a wooden frame from which
10 gutters have
been milled-out in such a way that each one can hold two alphabet rulers:
an upper one and a lower one.
The actual sliders, or rods, are constructed
in such a way that they slide smoothly
through the gutters without binding
or falling out. Two transparent windows
– with two black hairlines each – are
mounted to the frame at fixed positions. They mark the position of plain text
and cipher text (or vice versa).

Permutations

The device has 20 sliding alphabet rulers, 10 of which can be identified as the
upper alphabets, whilst the other 10 are the lower alphabets.This gives
10! (or 3,628,800) possible combinations 1 of alphabets for the upper half
only. As the same is true for the lower 10 alphabets, the total number of
combinations is 3,628,800 x 3,628,800, which is no less than:

13,168,189,440,000

Note that this result is only limited because the upper and lower alphabets
can not be mixed. This limitation was lifted in 1931 by Lugagne's employee
Paul Godillon, resulting in the successor of the Transpositeur –
Le Sphinx –
with a fenomenal 2,432,902,008,176,640,000 combinations.

Before exchanging a message by means of the Transpositeur,
both parties first have to agree which alphabet is used in each position.
This is done by quoting the red numbers that are printed at the end of
each rod. This is known as the
settings, or the key, and is usually pre-arranged between the
parties. For the default position, which we have used on this page, the
key would be:

1 2 3 4 5 6 7 8 9 0

1 2 3 4 5 6 7 8 9 0

Both users should now install the upper and lower alphabets in the order
given by the pre-arranged key. For the above one, the setup would be idential
to the storage position:

The Transpositeur is constructed in such a way that the user can slide
the rulers up and down manually.
There are two windows through which we can read a row of letters.
Now slide the rulers in such a way that the first 10 letters of the
plaintext
are visible in the upper window, e.g.:

TOPSECRETS

All you now have to do is read the
ciphertext
from the lower window, which in this case is:

RERPIBDOWB

All the receiving party has to do, is slide the rulers so that the ciphertext
is visible in the lower window. The original plaintext can now be read from
the upper window.

Despite the large number of possible arrangements of the alphabets,
Le Sphinx provides only low-grade cipher security. This is mainly caused
by the fact that the arrangment of the alphabets does not change during
the course of a message. If a message is long enough, it can be
solved by frequency analysis. For very short messages, the cipher would
be relatively secure though.

Another weakness of the system is that there is no provision for sending the
key at the start of a message. Instead, it has to be pre-arranged.
This was also the case with the German
Enigma cipher machine, although in
that case, procedures were in place to add a random message key.

Alphabets

The table below shows each of the 20 scrambled alphabets of our device.
Note that all alphabets are in a differently scrambled order.
Also note that the upper alphabets can not be mixed with the lower
alphabets. This can be seen as a cryptographic weakness, as it significantly
reduces the number of combinations. This problem was solved in 1930,
in improved device Le Sphinx.

1

JKYLMNAPQRESTVIWXZOBCDUFGH

2

WXAZBCEDFGIHJKOLMNUPQRYSTV

3

BCODFGUHJKYLMNAPQRESTVIWXZ

4

PQIRSTOVWXUZBCYDFGAHJKELMN

5

FGUHJKYLMNAPQRESTVIWXZOBCD

6

ZBECDFIGHJOKLMUNPQYRSTAVWX

7

CDOFGHUJKLYMNPAQRSETVWIXZB

8

RSATVWEXZBICDFOGHJUKLMYNPQ

9

HJIKLMONPQURSTYVWXAZBCEDFG

0

MNEPQRISTVOWXZUBCDYFGHAJKL

1

GHEJKLIMNPOQRSUTVWYXZBACDF

2

QRUSTVYWXZABCDEFGHIJKLOMNP

3

DFAGHJEKLMINPQORSTUVWXYZBC

4

LMENPQIRSTOVWXUZBCYDFGAHJK

5

STYVWXAZBCEDFGIHJKOLMNUPQR

6

XZUBCDYFGHAJKLEMNPIQRSOTVW

7

NPAQRSETVWIXZBOCDFUGHJYKLM

8

VWIXZBOCDFUGHJYKKMANPQERST

9

KLYMNPAQRSETVWIXZBOCDFUGHJ

0

TVOWXZUBCDYFGHAJKLENMPIQRS

Successor

Around 1930, the Transpositeur was succeeded by the similar
but improved device known as Le Sphinx. Like the Transpositeur
it had 10 double sliding alphabets, but these could be mixed.

Le Sphinx was made of aluminium rather than wood, and came in a
stylish bakelite storage case. Both devices are extremely rare.